Question

If , $\frac{a}{b}=\frac{c}{d}$
Whether the given equation : $\frac{3a^2+4b^2}{3c^2+4d^2}=\frac{3a^2-4b^2}{3c^2-4d^2}$ is ?

• A. True
• B. False

Answer 1

The correct option is A True

Given,

$\frac{a}{b}=\frac{c}{d}⟹a=\frac{bc}{d}$

Taking LHS

$\frac{3a^2+4b^2}{3c^2+4d^2}=\frac{3(\frac{bc}{d}{)}^2+4b^2}{3c^2+4d^2}$

$=\frac{\frac{b^2}{d^2}(3c^2+4d^2)}{3c^2+4d^2}=\frac{b^2}{d^2}-\left(1\right)$

Taking RHS

$\frac{3a^2-4b^2}{3c^2-4d^2}=\frac{3(\frac{bc}{d}{)}^2-4b^2}{3c^2-4d^2}$

$=\frac{\frac{b^2}{d^2}(3c^2-4d^2)}{3c^2-4d^2}=\frac{b^2}{d^2}-\left(2\right)$

From eqs.(1) and (2) we get

$LHS=RHS$